Triangle Congruence: Question 1
In the accompanying proof, what is reason (5)?
Given: A B║DC
AB=DC
Prove: m ∠DAC= m ∠BCA
Select one:
SSS
SAS
SSA
ASA

Answer:

141

Step-by-step explanation:

So we substitute x with 6

5*6^2+2*6-10

5*36+12-10

180+2

182

then substitute x with 3

5*3^2+2*3-10

5*9+6-10

45-4

41

now we find the difference

182-41=141

Answer:

the angle is equal to 60 degree

Answer:

The answer is $3750

Step-by-step explanation:

1500/x = 40/100

(100) × 1500 = 40x

150000 = 40x

x = 150000 ÷ 40

x = 3750

Thus, The minimum monthly income required by the lender is $3750.

-TheUnknownScientist 72

Given the following exponential equation:

For x = 0, we have:

Then, the y-intercept must be y = 2. Now, for x = -2:

Looking at D, we see that the y-intercept is 4, so this graph does not correspond to the equation. Looking at B and C, we see that y ≠ 8 for x = -2, so we discard them.

For A:

We see that y = 8 for x = -2, and the y-intercept is 2. Then, this is the corresponding graph of the equation.

Answer: A

Answer:

-x/x-2

Step-by-step explanation:

The future value of the annuity after the end of 5 years is $552.56.

Given that, r =5%= 0.05, 5 years  = 5 yearly payments, so n = 5, and P = $100.

The formula to find the annuity formula \(FV=\frac{P \times ((1+r)^{n}-1 )}{r}\).

Now, \(FV=\frac{100 \times ((1+0.05)^{5}-1 )}{0.05}\)

⇒FV = 100 × 55.256

⇒FV = $552.56

Therefore, the future value of the annuity after the end of 5 years is $552.56.

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Answer:

Johnathon bought 20 cookies because 20×4=80!

At a stock exchange, number of shares sold by Stock A is 4000, Stock B is 1000 and Stock C is 5000.

Total shares sold = 10000

⇒ A + B + C = 10000  …. (1)

Shares sold by Stock A = 4 × Shares sold by Stock B

⇒ A = 4B … (2)

Shares sold by C = Shares sold by stock A + Shares sold by stock B

⇒ C = A + B … (3)

Substitute value of A from (2) in (3)

⇒ C = 4B + B

⇒ C = 5B

Substitute the values of A and C in (1), we get

4B + B + 5B = 10000

⇒ 10B = 10000

⇒ B = 1000

⇒ A = 4 × 1000 = 4000

⇒ C = 5 × 1000 = 5000

Hence, the shares sold by Stock A is 4000, Stock B is 1000, and Stock C is 5000.

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Answer:

24

Step-by-step explanation:

The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.

6 x 8 = 48

48 / 2 = 24

By using the concept of number line, it can be calculated that

a) g is a function

b) g(5) = 3 means after 5 flips, the person is at '3' on the number line

c) Probability that g(3) = 0 is zero

What is a number line?

All the real numbers, integers, fractions can be pictorially represented with the help of a line. The line is known as number line.

a) Here, g represents the position after the nth flip

After n flips, a person stands at only one position on the number line, not more than one. So every point on the domain has unique image. So g is a function.

b) g(5) = 3 means after 5 flips, the person is at '3' on the number line

c) The person is initially standing at zero. To move to zero position, even number of flips have to be made. But 3 is not an even number. So probability that g(3) = 0 is zero

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Answer:

No solution

Step-by-step explanation:

You will get zero

Answer:

He did not control for lurking variables and their impacts on the results of his experiment. Amount of sunlight and water received are two outside variables(or confounding variables) that may impact the growth of his plants and influence the results. He needs to apply the same amount of sunlight and water to each plant within a different planting soil in order to rule out the influence of those two variables and test the sole effect of the soil brand on the plant growth. Otherwise, it would be hard to determine whether his plant growth was because of the soil brand or the different amounts of sunlight and water received

Answer:

Invalid

Step-by-step explanation:

Xavier did not control variables or the impacts of the results. Confounding variable being sunlight and water received are two outside variables that can impact growth influence results. Within a different planting soil, Xavier will apply the same amount of sunlight & water to each plant to rule out the influence of those two variables. The test for sole effect on the plant with growth otherwise be determine. Is the plant growth because of the soil brand or the different amounts of sunlight and water received? This could and will impaired the results of this experiment, therefore, making it invalid.

Answer:

$ 3750  = truck rental;   $125 per ton of sugar transported

C is cost;  S is number of tons transported

Equation relating C to S would be a linear equation like y = mx + b

C = 125S + $3750

This equation would be graphed in the first quadrant only

you would start with your y-intercept at (0, 3750)

As x increases by 1, your y increases by 125 yielding these points:

(1, 3875)  (2, 4000)  (3, 4125)  etc.  

This shows that for each increase by one ton of sugar, the cost goes up $125

Step-by-step explanation:

Answer:

Step-by-step explanation:

sum of angles in a triangle=180º

90+60x+30x=180

90+90x=180

90(1+x)=180

1+x=2

x=1

angle A=30º

Answer:

Step-by-step explanation:

The sum of the measures of angles DAC and CAB must equal the measure of angle DAB, since they are adjacent angles that share a common vertex, A. Therefore, we have:

(DAC) + (CAB) = (DAB)

Substituting the given values, we get:

(2y - 7) + (3y + 2) = (DAB)

Simplifying and solving for y, we get:

5y - 5 = (DAB)

y = (DAB + 5) / 5

Now we can find the measure of angle CAB by substituting y back into the given expression for CAB:

<CAB = (3y + 2) = 3[(DAB + 5)/5] + 2 = (3DAB + 17)/5

Therefore, the measure of angle CAB is (3DAB + 17)/5 degrees.

Answer:

The smallest 5 digit number is 10,000 and the greatest 5 digit number is 99,999. There are 90,000 five-digit numbers in all.

Answer:

Step-by-step explanation:

Step one:

given data

total ounces combined= 8.65+8.09= 16.74 ounces

We are told that the remainder after pouring the fruits into four bowls is

2.78 ounces, hence what was divided is

= 16.74-2.78=13.96 ounces

Now the amount that was divided is 13.96 ounces

hence a bowl took 13.96/4= 3.49 ounces

Answer:

60%

Step-by-step explanation:

15 out of 25 is 60%

25 is the total people in the club

Hope this helps

Answer:

x^3 + 2x - 1.

Step-by-step explanation:

To simplify the expression 2x + x^3 - 1, we can first rearrange the terms in decreasing order of the exponents:

x^3 + 2x - 1

So the simplified expression, rearranged in descending order, is x^3 + 2x - 1.

Answer:

n > 4

Step-by-step explanation:

7 * n/4 > 7

7n/4 > 7

7n > 7 * 4.....(multiply both sides by 4)

7n > 28

n > 4.....(divide both sides by 7 to isolate n)

Answer:

H

Step-by-step explanation:

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

2(15+8)

Step-by-step explanation:

Given the expression 30+16

We are to use GCF to rewrite the sum as a product.

Get the factor of each value first as shown;

30 = 2 * 15

16 = 2 * 8

substitute the factors back into the expression:

30+16 = (2*15)+(2*8)

Since 2 is common to both terms, then:

30+16  = 2(15+8)

Hence the required sum of product of the terms is 2(15+8)

The total value of the exponential expression is a³

What is Exponentiation ?

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.

Now, The given expression is :

a^3 (2a^2 + 4bc^4)^ 0

From the properties of exponents we know that:

a⁰ = 1

Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1

Hence,  The total value of the exponential expression is a³

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Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

The average score of the spelling test is 90.6%

To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.

First, let's add up all the scores:

2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265

Next, we divide by the total number of students:

Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%

Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.

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The correct statement that F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

To determine whether the function shown in the table is exponential, we need to analyze the relationship between the x-values and y-values.

The table shows x-values that are increasing by a power of 2 (1, 2, 4, 8, 16, 32, 64) and y-values that are increasing by a constant rate of 1 (0, 1, 2, 3, 4, 5, 6).

The constant ratio between consecutive x-values indicates exponential growth or decay.

In this case, the function is growing exponentially because the y-values are increasing at a constant rate.

Based on this information, we can conclude that the function is exponential.

Therefore, we agree with statement F: "I agree. The ratios of consecutive x-values are constant, and the y-values are increasing at a constant rate."

The other statements are incorrect because they do not accurately describe the relationship between the x-values and y-values in an exponential function.

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A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

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